Search

We present the first example of a rigorous uncertainty quantification on elastic Nucleus-Nucleus scattering at energies near the Coulomb barrier. Experimental data has been analyzed using an energy dependent effective optical model potential with physical constraints imposed. We confirm the compatibility of these uncertainties with the well known Coulomb threshold anomaly, explained in terms of a dispersive relation, and contrast our results with previous analyses that suggest otherwise., 6 pages, 3 figures

Five $\Xi^- p\to \Lambda\Lambda$ two-body capture events in $^{12}$C and $^{14}$N emulsion nuclei, in which a pair of single-$\Lambda$ hypernuclei is formed and identified by their weak decay, have been observed in $(K^-,K^+)$ emulsion exposures at KEK and J-PARC. Applying a $\Xi^-$-nucleus optical potential methodology to study atomic and nuclear transitions, we confirm that these capture events occur from Coulomb assisted $1p_{\Xi^-}$ nuclear states. Long-range $\Xi N$ shell-model correlations are found essential to achieve consistency between the $^{12}$C and $^{14}$N events. The resulting $\Xi$-nuclear interaction is strongly attractive, with $\Xi$ potential depth in nuclear matter $V_{\Xi}\gtrsim 20$ MeV. Implications to multi-strangeness features of dense matter are outlined., Comment: v4: 16 pages, 2 figures, 2 tables, agrees with published PLB version

Coherent forward neutron propagation in gas is discussed as a new approach to search for neutron-antineutron oscillations (n−n¯), which violate both B and B−L conservation. We show that one can increase the probability of neutron - antineutron transitions in the presence of a nonzero external magnetic field to essentially free neutron oscillation probability by tuning the density of an appropriate mixture of gases so that the neutron optical potential of the gas cancels that from the magnetic field.

Recent theoretical work has shown that spin $1/2$ particles moving through unpolarized matter which sources torsion fields experience a new type of parity-even and time-reversal-odd optical potential if the matter is spinning in the lab frame. This new type of optical potential can be sought experimentally using the helicity dependence of the total cross sections for longitudinally polarized neutrons moving through a rotating cylindrical target. In combination with recent experimental constraints on short-range P--odd, T--even torsion interactions derived from polarized neutron spin rotation in matter one can derive separate constraints on the time components of scalar and pseudoscalar torsion fields in matter. We estimate the sensitivity achievable in such an experiment and briefly outline some of the potential sources of systematic error to be considered in any future experimental search for this effect., Comment: 5 pages, no figures, to appear in Physics Letters B

The process e + e − → N N ¯ is studied nearby a threshold with account for polarizations of all initial and final particles. The nucleon polarization ζ N reveals a strong energy dependence due to that of the nucleon electromagnetic form factors G E ( Q 2 ) and G M ( Q 2 ) caused by the final-state interaction of nucleons. It is shown that the modulus of the ratio of these form factors and their relative phase can be determined by measuring ζ N along with the differential cross section. The polarization degree is analyzed using Paris N N ¯ optical potential for calculation of the form factors. It turns out that | ζ N | is high enough in a rather wide energy range above the threshold. Being especially high for longitudinally polarized beams, | ζ N | is noticeable even if both e + e − beams are unpolarized.

We propose a new technique to analyze total reaction cross sections. In this technique, which has been previously applied to fusion reactions, the experimental data are used to build a dimensionless reaction function, which does not depend on the system size or details of the optical potential. In this way, total reaction cross sections for different systems can be directly compared. We employ this technique to perform a systematic study of reaction cross sections of weakly bound systems in different mass ranges, and compare their reaction functions with the ones of tightly bound systems with similar masses. We show that breakup reactions and neutron transfers in halo systems lead to large reaction functions, well above the ones of typical tightly or weakly bound stable systems.

We use the Paris nucleon–antinucleon optical potential for explanation of experimental data in the process e + e − → p p ¯ near threshold. It is shown that the cross section and the electromagnetic form factors are very sensitive to the parameters of the potential. It turns out that final-state interaction due to slightly modified absorptive part of the potential allows us to reproduce available experimental data. We also demonstrated that the cross section in n n ¯ channel is larger than that in p p ¯ one, and their ratio is almost energy independent up to 2.2 GeV.

The kaon nuclear optical potential is studied including the effect of the $\Theta^+$ pentaquark. The one-nucleon contribution is obtained using an extension of the J\"ulich meson-exchange potential as bare kaon-nucleon interaction. Significant differences between a fully self-consistent calculation and the usually employed low-density $T\rho$ approach are observed. The influence of the one-nucleon absorption process, $K N \to \Theta^+$, on the kaon optical potential is negligible due to the small width of the pentaquark. In contrast, the two-nucleon mechanism, $K N N \to \Theta^+ N$, estimated from the coupling of the pentaquark to a two-meson cloud, provides the required amount of additional kaon absorption to reconcile with data the systematically low $K^+$-nucleus reaction cross sections found by the theoretical models., Comment: 9 pages, 6 figures. Extended discussion on absorption and reaction cross sections. Accepted in Phys. Lett. B

We present results on the production of bound states of Θ + in nuclei using the ( K + , π + ) reaction. By taking into account the states obtained within a wide range of strength of the Θ + nucleus optical potential, plus the possibility to replace different nucleons of the nucleus, we obtain an excitation spectra with clearly differentiated peaks. The magnitude of the calculated cross sections is well within reachable range.

The energy dependence of chirally expanded pi N isoscalar and isovector amplitudes b_0(E) and b_1(E) respectively, for zero-momentum off shell pions near threshold, is used to impose the minimal substitution requirement E -> E - V_c on the properly constructed pion optical potential within a large-scale fit to 100 pionic-atom data across the periodic table which also include the recently established `deeply bound' pionic atoms of Pb and Sn. This fit cannot be reconciled with the well known free-space values of the pi N threshold amplitudes. In contrast, introducing the empirically known energy dependence for on-shell pions leads to a better fit and to satisfactory values for the pi N threshold amplitudes. The difference between these two approaches is briefly discussed., 10 pages, 3 figures, submitted to PLB. Discussion section rewritten, omitting an erroneous equation. Results and conclusions unchanged Accepted by PLB

The structure of 6 He is explored with proton elastic and inelastic scattering to the first 2 + excited state (Q =− 1. 8M eV) of 6 He in the inverse kinematics using a 24.5 A MeV 6 He beam. The distorted wave approximation (DWA) with an optical potential obtained by folding an effective nucleon–nucleon (NN) g-matrix with the 6 He density matrix elements as given by a large basis shell model is used to analyse the data. The comparison of predictions with the data confirms the view that 6 He has

Elastic differential cross sections for K + mesons scattered from nat C and 6 Li targets have been measured at an incident momentum of 715 MeV/c and at angles of 7° to 42° in the laboratory frame. The experimental cross sections agree, within errors, with two different parameter-free impulse approximation calculations. To reduce the effects of the systematic errors, the ratio of the experimental cross sections for nat C to 6 Li is compared to the theoretical values, and these ratios do not agree with theory. This discrepancy suggests either a density-dependent alteration of K + -nucleon amplitudes or a failure of the optical potential calculations to describe these nuclides adequately.

In the present work, we test the validity of replacing the non-diagonal density matrix appearing in the exchange part of the nucleus-nucleus optical potential by an approximation based on the density matrix expansion used frequently in the nuclear structure calculations. We have found that for the recently derived BDM3Y nucleon-nucleon force the DME may produce a maximum error more than 20% in the nucleus-nucleus potential.

We have measured the elastic scattering angular distribution for the 16 O + 16 O system at Elab = 124 MeV, where a prominent minimum has been observed in the θcm = 90° excitation function. The measured angular distribution shows modulated Airy structures at large angles with a dip at θcm = 90°. It is concluded that the prominent minimum in the excitation function is due to an Airy minimum, most likely to be the third member, crossing 90° at that energy.

The elastic 11 Li, 11 C+ 12 C scattering at E A ∼- 60 MeV has been studied using a semimicroscopic version of the optical model. The real optical potential was calculated within the double-folding model using a realistic nucleon-nucleon effective interaction and a more accurate treatment of the knock-on exchange. A Hartree-Fock density was taken for 11 Li, while the shell model was used for 11,12 C. The imaginary potential was taken in standard Woods-Saxon form. The dynamic polarization potential due to the breakup effect, based on the results of realistic four-body calculations of the 11 Li+ 12 C scattering, has been added to both the real and imaginary potentials for 11 Li. From different assumptions about the absorptive strength at the surface region, we found a set of parameters which give a reasonable description of the quasielastic 11 Li, 11 C+ 12 C scattering data at E A ∼- 60 MeV as well as reproducing the observed trend for the total reaction cross section at higher energies.

Effective Lagrangians involving nucleons coupled to scalar and vector fields are investigated within the framework of relativistic mean-field theory. The study presents the traditional Walecka model and different kinds of scalar derivative coupling suggested by Zimanyi and Moszkowski (ZM). It is shown that the equations of state for all these modified ZM models are soft. The real part of the optical potential for these models is obtained. When compared with the usual ZM model, the modified models present the peculiarity of giving simultaneously a smaller nucleon effective mass and a smaller incompressibility. This can be explained through the mesonic nonlinear scalar-vector coupling contained in these modified models.

It has been reported that the excitation of low-lying 3 − states in nuclei by hadronic probes indicate much weaker transition strengths than are implied by the results of electromagnetic measurements. We demonstrate that this is a consequence of using the deformed optical potential model to analyze the hadronic scattering. The apparent hindrance disappears when a folding model is used. The discrepancy between the results of using the two models increases dramatically as the multipolarity of the transition increases, and we recommend the folding approach.

It is shown that the variation of the one- and two-nucleon transfer probability with distance can be understood on the basis of semiclassical models if the contributions from the nuclear and Coulomb branches of the classical deflection function are considered. A shallow potential, with a diffuseness parameter a = 0.8–0.9 fm for the real part of the heavy ion optical potential, was found necessary to understand the data.

The charge-exchange reaction 12C(12C, 12N)12B has been studied at E A = 135 MeV . The elastic scattering of 12C from 12 C was also measured to determine the optical potential parameters. The differential cross sections for the charge-exchange reaction leading to the 12B ground state (1+) were well described byh the microscopic DWBA calculation, suggesting the dominance of the one-step process. The L = 0 component was found to be about five times stronger than the L = 2 component at 0°.

We show that a recent model of medium modifications of the ππ scattering amplitude leads to a new source of repulsion in the S-wave pion optical potential, which existing models are unable to explain. Our result indicates that pions do not condense through S-wave interactions.

We study phenomenologically the density dependence of the K − optical potential V opt ( r ) at zero kinetic energy by fitting it to a comprehensive set of atomic data across the periodic table. Two families of solutions offer improved fits over that for the standard t eff ϱ ( r ) paraameterization of V opt . One family contains solutions for V opt with RMS radii larger than those of the matter density ϱ , as expected from finite-range folding corrections. The other family offers substantially improved fits to the data and gives rise to Re V opt of a size smaller than that of ϱ . The new family contains solutions for which V opt is attractive inside the nucleus and on its surface, becoming repulsive at large distances. The repulsion can be made to approximately agree with the low-density limit V opt → tϱ where t is the free-space K N t matrix. It is argued that this sign flip might be expected from the underlying nuclear propagation of the Λ(1405).

The basic nuclear matter properties are calculated within the standard Hartree-Fock scheme using a Michigan version of the in-medium NN interaction (the so-called M3Y interaction). Due to the attractive character of the M3Y interaction, the saturation requirement for the nuclear matter is not fulfilled and the nuclear matter generated with this interaction is unstable against collapse. This necessitates the introduction of an appropriate density dependence into the original M3Y interaction. Our density dependent versions of the M3Y interaction consistently reproduce the equilibrium density and binding energy of the normal nuclear matter as well as the microscopic results (obtained by Jeukenne, Lejeune and Mahaux) for the nucleon optical potential. They can be used in the folding model to calculate the nucleon-nucleus and nucleus-nucleus potentials. A possible study of the cold nuclear equation of state through heavy-ion scattering, which is based on the use of the new interaction to calculate the heavy-ion optical potential, is also discussed.

Correlated basis function calculations of the binding energy, the optical potential and the self-energy of nuclear matter models based on the Argonne ν 14 interaction are presented. The results obtained are compared with the existing correlated basis calculations performed for corresponding models based on the Urbana ν 14 potential. The two potentials lead to significative differences in the self-energy and related quantities. The results show an overall agreement with calculations based on Brueckner-Hartree-Fock theory.

A quantal inversion of the 16O-16O scattering data at 350 MeV yields an optical potential which gives an excellent fit ( χ 2 F =1.65 ) to the measured cross-section. The real part of this potential is shallower than any potential used by others for distances between 2 and 6 fm. The imaginary potential is also relatively weak. This potential does not favour a rainbow interpretation of the structure in data observed at large scattering angles.

Using an inversion procedure for the SO(3,1) algebraic potential the best shape for reproducing the S l matrix elements of a Woods-Saxon potential is determined. The algebraic optical potential thus found is applied to the elastic scattering of 12 C+ 24 Mg at E LAB =24.8, 27.7, 31.2, 34.8, 37.8 and 40.0 MeV.

We show that the imaginary parts of a pionic-atom optical potential cannot be a candidate, by themselves, for the explanation of the anomaly problem, when two-nucleon absorption is assumed to be described effectively by quadratic forms of nuclear densities. By examining multinucleon absorption processes, we find a criterion that will help to determine whether a potential fit to pionic-atom data (especially to anomalous data), is acceptable.

The elastic scattering of 16O+16O at 350 MeV has been reanalyzed using more general optical model potential shapes in an attempt to resolve the ambiguity over the order of rainbow seen in the angular distribution. We conclude that probably it is the primary rainbow, determining the real potential to have a volume integral Jv≈295±MeV fm3. However, the use of real potentials with non-monotonic shapes defined by splines does still allow the possibility of it being the secondary rainbow generated by a deeper potential. In addition, the use of splines introduces a more shallow potential which also implies observation of the primary rainbow.

The effects of the nuclear medium on relativistic optical potentials in nuclear matter are studied within the framework of the Dirac-Brueckner method. The medium effects are classified into Pauli blocking, dispersive, and Dirac spinor modification effects, where the last is shown to be most sizable and persistent up to high energies. Various meson exchange contributions to the spinor modification effect are investigated. It is shown that pionic contributions to the optical potentials are suppressed because of medium effects.

A theoretical study is done to see how the properties of deeply bound pionic atoms depend on the neutron skin. With increased neutron skin, the strong isovector part of the pion-nucleus optical potential helps developing a repulsive bump at the nuclear surface which pushes the pionic wave function further out and decreases the binding energy. With further increase of the neutron skin, the repulsive potential in the central part is reduced and an inner component of the wave function develops in the nuclear interior, and ultimately a pion bounds state of large width is formed in the deeper interior for Rn−Rp⩾ 0.35 fm.

We have reanalysed the recently observed nuclear rainbow data for the 16O+16O system and have demonstrated that there are three optical potentials which fit the data equally well. This discrete ambiguity originates from the limited angular range of the data. By taking into account the results of a recent analysis of low-energy resonant phenomena in this system and the dispersion relation between the real and imaginary parts of the optical potential, a unique selection of the potential set can be made.

The known proximity force approximation for the real part of the optical potential for two nuclei of radii R1 and R2 at distance R is extended to its imaginary part V I , calculated in the local nuclear matter approach. In this approximation V I /[R 1 R 2 / (R 1 + R 2 )] is a universal function of R−R1−R2 and energy. This scaling law is tested in the frivolous model, and also compared with recent empirical result for V I.

The rescattering contribution to the second-order S-wave pion-nucleus optical potential is calculated in a model of nuclear medium polarization which includes nucleon-hole-pair contributions as well as those of isobar-hole pairs. The resulting value for ( b 0 ) effective is found (for g ′= 0.6) to be in excellent agreement with that obtained in recent fits to pionic atom 1s level shift data for the fitting scenario which takes Re B 0 = 0.

The unique features of low-energy neutron scattering have been used to observe an lJ -dependence of the depth of the real volume optical potential near threshold for 208 Pb + n. At E = 0.5 MeV the s- and d-wave potentials are ∼ 3 MeV deeper than those for the p waves.

The scattering of 20 MeV polarized deuterons exhibits a phase behaviour between the angular distributions of elastic and inelastic scattering, which reflects the rather high transparency of the deuteron optical potential. For nuclei with closed shells we find phase relations which are opposite to the Blair rules for strongly absorptive probes. For deformed nuclei pronounced angular shifts are observed, which originate from the static mass quadrupole moment Q (2 + 1 ).

The pionic 2p→1s transition has been observed in Mg. For the strong interaction monopole shift a value has been measured of ϵ 0 (1s)=−81.6±0.6 keV with respect to the point Coulomb energy, in agreement with standard optical potential predictions. The observed strong interaction absorption width is Γ 0 (1s)=17.2±1.6 keV, which is about a factor of 1.5 smaller than expected from presently available models. This measurement confirms the trend of “anomalously” small strong interaction widths for deeply bound pionic states already observed in heavier elements.

An optical potential using kinematic, absorption and correlation corrections is applied to the scattering of 50 MeV pions by 12 C, 40 Ca, 90 Zr and 208 Pb. Each effect is found to be important.

The near cancellation of the pi-nuclear contributions from the lowest order non-linear terms in the Weinberg chiral lagrangian for pion-nucleon systems is re-examined in the presence of nuclear medium polarization in a popular model for these corrections. It is demonstrated that this near cancellation persists to all orders in isobar-hole pairs in spite of the further enhancement of the already large individual contributions to the S-wave pion-nucleus optical potential.

It is noted that the energy-independent optical potential yields both scattering and bound state solutions, and that this potential must be asymmetric to yield a spectroscopic factor different from unity.

A microscopic, momentum space, optical potential calculation of elastic p-4He scattering is compared with 100–200 MeV data over the full angular range. The least sophisticated potential explains the occurrence and energy dependence of the back angle peak.

A new effective nucleon-nucleon interaction gives the real part of heavy-ion optical potential tails correctly when used in a folding model. Exchange effects are discussed.

A pion-nucleus optical potential is derived using a relativistic πN amplitude and a Dirac Hartree-Fock description of the nucleus. For low-energy pion-nucleus scattering very large corrections to the standard theory are obtained.

The influence of momentum and frequency dependence of the nuclear mean field Σ on the level density parameter a is studied. By introducing a local quasiparticle effective mass we determine the volume, surface and curvature coefficients of a, expressed as a = a V A + a S A 2 3 + a c A 1 3 . It is found that the magnitude of ac is significant due to the very nature of the surface. A purely momentum dependent field Σ determined from the nonlocality of the optical potential gives a level density close to a self-consistent Thomas-Fermi description with Skyrme III forces. An explicit frequency dependence of Σ mainly influences as, enhancing it considerably for medium and heavy nuclei.

A method is described for determining the strength of the complex central optical potential directly from neutron total cross sections measured below the threshold for inelastic scattering. Real and imaginary strengths deduced for 208 Pb are consistent with higher-energy results and are shown to provide a good fit to above-threshold data.

The imaginary part of the relativistic optical potential is calculated in the Walecka model for nuclear matter. Large imaginary Lorentz scalar and vector contributions are found each of order 100 MeV (at 180 MeV incident energy). These agree well with phenomenological relativistic optical model results.

The Lorentz-Lorenz effect in pion-nucleus interactions is derived from the Watson expansion of the optical potential. The use of a realistic, finite range π N interaction significantly reduces its importance for nuclear short-range correlations in pionic atoms.

It is shown that the anomalous energy shifts in heavy pionic atoms may be explained by a gauge-generation of Coulomb terms in the s-wave π-nuclear optical potential without resorting to the energy dependence of the elementary amplitudes. The comparison with experiment is made in the “standard” π-nuclear optical model whose parameters most closely agree with the microscopic theory. The anomaly persists for the widths.

A nuclear optical potential acting on the Λ hyperon is evaluated within the framework of the G -matrix theory and the local density approximation by employing the Nijmegen OBE model D interaction.

We examine how different types of form factors for p -nucleus optical potential affect the analysis of X-ray data in p -atoms. We also study the effect of L·S force due to strong interaction in p -atoms.

The method of correlated orthogonal states is used to study the longitudinal and transverse response of 3 He and 3 H. The treatment of the d + N final states is improved by including a real d-N optical potential. The effects of short range correlations, orthogonality corrections, and d-N interaction in the final states bring the theoretical 3 He longitudinal and transverse, and 3 H transverse response functions into reasonable agreement with experiment, although a systematic lack of strength persists in the calculated 3 H longitudinal response at low ω.